perplexus.info :: Numbers : Find all Numbers II

Find all Numbers II (Posted on 2022-04-24)

Determine all possible value(s) of a non-leading zero, 5-digit positive integer N that satisfy each of these given conditions:
(i) Product of the digits of N is equal to the sum of its digits.
(ii) N is divisible by the sum of its digits.
(iii) N does NOT contain the digit 3.

Added for completeness:
What is the total number of values of N if we disregard condition (iii)?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required solution for N is 22112.
Somewhat interestingly, only one number with fewer than 5 digits meets the other criteria: it is 4112
Disregarding condition (iii), then there are 11 solutions. The other 10 solutions are the combinations of any 5-digit number composed of three 1's and two 3's.
For an explanation, refer to the solution submitted by:
• Brian Smith in this location.
• Larry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2022-08-02 10:09:40
Solution	Brian Smith	2022-04-24 10:07:27
Solution	Larry	2022-04-24 09:52:46
computer solution	Charlie	2022-04-24 09:42:46

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